Program Description: Purpose ofproblem is to construct a table for the approximation solution and the actual solution of y ′ = − y up to five decimal places by the use of RungeKutta’s method. Summary Introduction: Purpose will use RungeKutta’s method to construct the table of the approximation solution and the actual solution y = y ( x ) is the solution of a differential equation d y d x = f ( x , y ) with y ( x 0 ) = y 0 where approximate value can be calculated with the formula y i + 1 = y i + k ⋅ h and the value of k can be calculated as k = 1 6 ( k 1 + 2 k 2 + 2 k 3 + k 4 ) where the value of k 1 = f ( x i , y i ) , k 2 = f ( x i + 1 2 h , y i + 1 2 h k 1 ) , k 3 = f ( x i + 1 2 h , y i + 1 2 h k 2 ) and k 4 = f ( x i + 1 , y i + h k 3 ) .

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Chapter 2.6, Problem 7P

Program Plan Intro

Program Description: Purpose ofproblem is to construct a table for the approximation solution and the actual solution of y′=−y up to five decimal places by the use of RungeKutta’s method.

Summary Introduction:

Purpose will use RungeKutta’s method to construct the table of the approximation solution and the actual solution y=y(x) is the solution of a differential equation dydx=f(x,y) with y(x0)=y0 where approximate value can be calculated with the formula yi+1=yi+k⋅h and the value of k can be calculated as k=16(k1+2k2+2k3+k4) where the value of k1=f(xi,yi) , k2=f(xi+12h,yi+12hk1) , k3=f(xi+12h,yi+12hk2) and k4=f(xi+1,yi+hk3) .

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